A comparison of downwind sail coefficients from tests in different wind tunnels

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A comparison of downwind sail coef

ﬁcients from tests in different

wind tunnels

Ian Mortimer Colin Campbell

Wolfson Unit MTIA, University of Southampton, UK

a r t i c l e i n f o

Article history:

Received 8 November 2013 Accepted 24 June 2014 Available online 25 July 2014 Keywords: Sail coefﬁcients Wind tunnel Tests Yachts

a b s t r a c t

This paper contains results fromfive different tests on model sailing yacht rigs and sails. The tests were conducted by the author in four different wind tunnels over afifteen year period between 1991 and 2007. The tests were conducted as part of development programmes for Whitbread 60 and America's Cup Class yachts and for particular racing teams. They were originally subject to commercial confidentiality so have not been published previously.

Although the aim of the original tests was to compare sail designs and develop the performance of the individual yachts the aim of this study is somewhat different and uses the data to compare wind tunnels. The paper describes features of the wind tunnels that affect the results together with the test requirements for investigation of downwind sailing performance. A large number of individual results are presented from tests over a range of apparent wind angles and curves of maximum lift and drag coefﬁcients from each tunnel are then compared.

Although the original tests were not designed for benchmarking wind tunnels the lift coefficients from the different tests showed broad similarity within a 10% tolerance band and the drag coefficients within 20%. The difference between the tolerance bands being partly attributed to the dependence of induced drag on the square of lift. These together with similarities in the trends of the coefficients with apparent wind angle help validate the technique of wind tunnel testing of sailing yacht rigs. Conclusions have also been drawn from the results about the effect of lift on the drag of downwind sails and the overall accuracy of wind tunnel tests on rigs.

1. Introduction

The Wolfson Unit MTIA’s archives contain a large body of commercially conﬁdential data from wind tunnel and other tests. The results presented in this paper have been abstracted fromﬁve different wind tunnel sail test projects, selected to enable results from different wind tunnels to be compared. Permission to publish the results was kindly given by the clients.

Even though only one or two comparable sail conﬁgurations were selected from each of the _{ﬁve test programmes there} remained a large amount of data to condense into this paper, which provides the basis for a reasonably rigorous evaluation of downwind sail wind tunnel testing.

The tests were originally conducted to aid the development of the individual yachts and their sails and relative results between sails were consistent within each test. The aim of this paper was to examine consistency between different wind tunnel tests.

The sail coefﬁcients presented in this paper are the original values obtained at the time of each test, they have not been re-analysed or corrected to improve correlation as a result of the analysis performed for this paper. Comments are given in this paper where corrections may be applicable and future collabora-tions between wind tunnel organisacollabora-tions may help identify correc-tions for sail testing (e.g.Viola and Flay, 2011; Tahara et al., 2012).

2. Wind tunnels

The four wind tunnels used together with the year of the test were:

1994, Volvo automotive tunnel, Gothenburg, Sweden.Nilsson and Berndtsson, 1987.

1991, former Marchwood Engineering Laboratory (MEL) wind engineering tunnel, Southampton, UK.Robins, 1978.

1996 and 2003, University of Southampton (Soton) aeronautical tunnel, UK.

2006, Politecnico di Milano wind engineering tunnel, Bovisa, Italy.

Contents lists available atScienceDirect

journal homepage:www.elsevier.com/locate/oceaneng

Ocean Engineering

http://dx.doi.org/10.1016/j.oceaneng.2014.06.036

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The principle features of the tunnels that could affect the sail tests are given inSection 6.

3. Tests

Two of theﬁve tests from which results have been abstracted were of Whitbread 60 yachts (W60), developed for Round the World races. The other three tests were of America_{’s Cup Class} yachts of different versions; both IACC and ACC.

The W60, IACC and ACC yachts were similar, being single masted sloop rigs with asymmetric gennakers set from spinnaker poles. There were differences: fractional and masthead sails were tested on the W60s and mainsails were developed during the period of the tests with increasing leech roach leading to squared headed sails. Results are presented from both W60 and IACC yachts tested in the Soton tunnel so the effect of these differences on the sail coefﬁcients can be seen.

4. Downwind sailing angles

The apparent wind angles for downwind sailing vary depend-ing on the course, the size and performance of the yacht, its boat speed and the true wind speed (Wright et al., 2010).

For windward/leeward courses, such as the America’s Cup races in the IACC and ACC Classes the optimum true wind angles were

β

tw¼1507101, with an associated mean gybe angle of 601. VPP calculations provide the optimum true wind angle (

β

tw) and associated apparent wind angles (

β

aw), however these are obtained from the simple solution of the wind triangle, as illustrated inFig. 1. It can be seen that the apparent wind angle is dependent on the ratio of boat speed to true wind speed (Vs/Vtw) and varies between 601 and 1201 for ratios between 1.15 and 0.58. The boat speed tends to be higher than true wind speed in light winds and lower in stronger wind speeds because of the non-linear relation-ship between hydrodynamic resistance and aerodynamic thrust.

It is therefore necessary to test downwind sails through a wide range of apparent wind angles, although there may be different sails designed for different ranges of angles. Similar apparent wind angles can occur at lower true wind angles associated with reaching, although they tend towards 601 and lower. Downwind sailing is, however, characterised by low heel angles, typically less than 51 for the ACC yachts, whereas reaching performance can cause signiﬁcant heeling. The maximum driving force is of primary interest for downwind sail testing, with the heeling moment having little effect on sailing performance. This is different from upwind and reaching where depowered sail settings are of importance for sailing in moderate and strong wind conditions.

Downwind sailing at an apparent wind angle of 901 is an interesting condition, which for America’s Cup Class yachts sailing arose in a true wind speed of 12 knots– the mid wind range for good sea breezes in Valencia Spain, the location for AC32 and AC33 America’s Cup races. At this angle all the driving force was derived

from aerodynamic lift and all the heeling force from drag so maximum driving force equated to maximum lift.

At deeper apparent wind angles the lift force contributed to the righting moment as opposed to contributing to the heeling moment at closer or smaller apparent wind angles. The heeling moment tended to zero at an apparent wind angle of 1351, where the righting moment from the lift force balanced the heeling moment from the drag force or in other terms where the resultant aerodynamic force was aligned with the boat axis.

5. Data reduction

The measured forces can be expressed in various ways and although a yacht’s performance depends principally on driving force and heeling moment in the body axis it is better to compare sail aerodynamics in conventional lift and drag coefﬁcients in the wind axis. These are used in VPP calculations and show less variation with apparent wind angle than forces in the body axis.

Drag coefficient Cd¼ D=1=2

ρ

Vaw2_A _ð1Þ

Induced Drag coefficient Cdi¼ ACl2

=

π

He2 _ð2Þ

Induced drag Di¼ L2

=1=2

ρ

Vaw2He2 ð3Þ

The reduction of measured forces to aerodynamic coefﬁcients depends on apparent wind speed (Vaw) or the associated dynamic pressure and sail area (A). The Induced drag due to lift is dependant on the Effective Rig Height (He) and measurement accuracy of these parameters is discussed in separate sections of this paper but the inﬂuence of any differences between the tunnels is discussed here.

Relative results between sails tested in one tunnel remain unaffected by errors in the wind speed measurement, provided it is taken in a consistent manner. Scaling to the yacht’s perfor-mance depends on the wind speed measurement for the yacht as well as that in the tunnel, which is also problematic since measurements for the yacht are generally obtained from a mast-head anemometer that is particularly affected by mastmast-head down-wind sails and by the prevailing down-wind gradient.

Both the lift and drag coefficients would appear to be affected similarly by differences in wind speed but this does not apply to the induced drag due to lift. It can be seen from Eq. 2that the induced drag coefficient depends on the square of the lift coeffi-cient and the aspect ratio, which has been expressed as He2_/A

where He is the effective rig height – a distance related to the geometric rig height (Teeters et al., 2003). The effective rig height is a useful parameter to derive because, as shown in Eq.3, it is independent of sail area but its correct determination relies on the correct measurement of dynamic pressure. This can cause differ-ences when comparing effective rig heights from tests in different wind tunnels.

6. Sail areas

Both the America’s Cup Class Rule and the Whitbread 60 Class Rule had sail measurements designed to produce the surface area of the sails. There were differences in the details of the measure-ments but the differences between the actual and measured surface areas of the sails will have been relatively small, within a few per cent. Details of the measurements are given in the published class rules.

The sail coefﬁcients given in this paper are based on the Rule measurements of sail area and not the planform or projected areas

150°

120°

60°

Vaw=0.58Vtw

Va

_w

Vs=1.15Vtw

Vtw

Vs=0.58Vtw

tw

aw

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that are sometimes used in the deﬁnition of lift and drag coefﬁcients of other bodies in different applications (Table 2).

7. Wind speed measurements

The four tunnels had different wind circuits that affected the wind speed proﬁles and their measurements. Sail tests require relatively large working sections and low wind speeds compared to convention aeronautical testing. The working test section in conventional aeronautical wind tunnels is downstream of a larger section of the tunnel with a contraction, which improves theﬂow uniformity and reduces the turbulence intensity. But there were no contractions immediately upstream of any of the sections used for these tests because of the requirement for a large working section.

The Volvo wind tunnel had a long lead upstream of the working section so the model was approximately 25 m down-stream from the last corner and approximately 10 m from the start of the slotted wall test section. Theﬂow uniformity was very good with variations in pitot pressure of 70.2%. The boundary layer

δ

thickness was approximately 80 mm.

The model in the low speed section of the University of Southampton wind tunnel was only approximately 2 m from the last corner and its associated smoothing screens. An additional screen was_{fitted prior to the W60 tests with the aim of improving} theflow uniformity. This had a static pressure drop of twice the dynamic pressure, which was suitable for use in wind tunnels. The flow, however, was not as uniform as the in the Volvo tunnel and there were consistent variations of dynamic pressure across the model’s location with an rms value of 5%. The flow in the high speed section, which was downstream following a contraction with a 5:1 area ratio, was much more uniform and the reference speed for the tests was taken from this section. The boundary layer was within 150 mm from the tunnelfloor.

The tunnels at the Marchwood Engineering Laboratory and the Politecnico di Milano were designed for wind engineering work so had long sections used to grow a stable boundary layer ﬂow to model that of the atmosphere, albeit at a scales at least an order of magnitude smaller than those of sail test models.

The MEL wind tunnel was open circuit with a bell mouth intake that drew air from the outside environment into the enclosed working section. The inlet wasfitted with screens to help isolate theflow in the test section from the external wind environment but some sensitivity remained. The air was drawn down the working section by a single 1 MW centrifugal fan and exhausted back outside. The tunnel was reported to have suffered from a slow oscillation in its wind speed, likened to an organ pipe effect, but sail force measurements were averaged over a period of approximately 1 min such that any oscillations did not affect the results, evidenced by good repeatability. The tunnel floor was covered with toy lego brick blocks to increase its roughness and create a boundary layer, which extended to a height of approxi-mately 500 mm. Theflow speed remained consistent within the boundary layer and was measured using a pitot tube within the working section.

The Politecnico di Milano wind tunnel had a closed circuit, with a bank of fourteen fans driving the air through thefinal bend into the low speed section. The tunnel floor was smooth and the boundary layer was approximately 300 mm thick but there were consistent lateral and vertical variations inflow speed across the location of the model. These were associated with theflow pattern from the individual fans and amounted to an rms variation in pitot pressure of approximately 5%. The tunnel had a high speed section on the return circuit below the low speed section with a contrac-tion ratio of approximately 3:1, which helped produce a relatively

uniform speed in this smaller section. So to avoid the problems with the _{flow variations and effects from the presence of the} model the meanflow speed was taken from measurements in the high speed section. This method of speed measurement was also used in the University of Southampton wind tunnel but the absolute accuracy of the speed measurement relied on a correla-tion factor between theflow in the boundary layer within the low speed section and theflow measurement point in the high speed section. This is a potential source of error in the comparison of sail coefficients from different wind tunnels.

Examples of theﬂow measurements taken at the time of the wind tunnels test at the location of the model are shown inFig. 2 together with the apparent wind gradient for the 1:12.5 scale ACC yacht model tested in the Politecnico di Milano tunnel. Uneven-ness in the wind pro_{ﬁle can be seen in data from this and the} Southampton tunnel but it should be noted that the mean test speed was derived from a grid of measurements taken across the test area not just those shown inFig. 2.

Reduced wind speeds over the lower part of the model sails were most signiﬁcant in the MEL tunnel.

The wind speeds used for the downwind sail tests were approximately 5 m/s. This was within both the structural strength of the model and the power of the remotely operated sheet winches. It also matched the scale relationship between the wind pressure and sail cloth weight, ensuring reasonable modelling of theflown sail shapes. The test Reynolds numbers were conse-quentially less than full scale by the order of the model scale, i.e. a factor of at least 12.5–20 lower than full scale. This is an unavoid-able feature of model testing and the low Reynolds numbers could affect the extent of the laminar boundary layer over the sails and both laminar and turbulent boundary layer separation zones, with the potential for them to be more extensive than full-scale. It is possible that these effects could result in lower maximum lift coefficients and higher drag coefficients than full-scale but the relationships between model-scale and full-scale results is outside the scope of this paper, although the results presented can be used by others to compare with full-scale data (Table 1).

8. Wind gradient and twist

The apparent wind speed gradient and twist that is experi-enced by the yacht when sailing depends on the true wind gradient and the yacht’s speed and heading. This involves solution of the wind triangle shown inFig. 1with height.

Apparent wind gradient and Tunnel boundary layer measurements

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.4 0.6 0.8 1.0 1.2

Speed ratio U/U10m

Height ratio Z/Z10 m Baw=90 1/20 power MEL 1:20 scale Milano 1:12.5 scale Soton 1:18 scale

ACC mast height

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Tests with a twisted ﬂow device, Zasso et al., 2005, were conducted in the Milano tunnel for the America’s Cup using a true wind gradient measured in Valencia for the prevailing sea breezes. The gradient was curveﬁtted by a power law of between 1/20 and 1/30, which was considerably lower than the conven-tional 1/7 or 1/10 curves. The associated apparent wind gradients and twist for a 1/20 true gradient are shown inTable 3for different ratios of boat speed (Vs) to true wind speed (Vtw), which correspond to racing conditions for downwind sailing at a true wind angle of

β

tw_{¼1501 (}Table 2).

Considerable twist occurs below boom level, where it has little inﬂuence on the sails and its effect on modelling in the wind tunnel is on hull windage. It can be seen that the twist at the boom was only slightly greater than at the masthead. After some adjustments of the vanes in the wind tunnel, similar twist was achieved at the boom and mast of751.

It can be seen from Table 3 that the actual apparent wind gradient at sea is relatively small at high boat speed ratios, which are associated with light winds. So these conditions are reasonably represented by the uniform wind speeds in the Soton and Volvo tunnels. The wind gradient in the Milano tunnel, shown inFig. 2, was representative of medium wind sailing conditions with apparent wind angles of 75–1081. The deep boundary layer in the MEL tunnel was less representative of the downwind sailing conditions, which is not surprising as the tunnel was designed to model the true atmospheric wind gradient for building work not the apparent wind gradient produced by a moving yacht.

9. Blockage corrections

The most signiﬁcant correction for downwind sail measure-ments made in closed jet test sections is the wake blockage correction. This corrects for the reduced pressure, i.e. higher suction, in the wake resulting from the tunnel wall constraints on the streamlines downstream of the model. The so-called Maskell correction was applied to some of the tests using the method given in ESDU data sheet 80024. The correction is based on the drag due to separatedﬂow, obtained by subtracting of the induced drag due to the measured lift. Although the wake

blockage is calculated from the measured drag the correction is of the base pressure acting on the sails so is applied to both lift and drag forces.

Wake blockage corrections were studied by the automotive industry in the 1980s, when manufacturers were vying to produce low drag coefﬁcients for their cars and the Volvo tunnel was designed with slotted walls in an attempt to overcome the problem. The test section has similarities with an open jet tunnel, where blockage corrections are applied in the opposite sense due to less suction of the wake, but at the time of the tests blockage corrections were not applied to the sail test results from this tunnel.

The MEL tunnel was relatively large compared to the South-ampton tunnel so at the time an average estimate of the wake blockage correction was applied to all results. The analysis process was reﬁned for subsequent tests such that corrections were calculated for individual test points. The maximum correction factors used for the tests in this paper are shown inFig. 3.

It can be seen that the wake blockage corrections in the Southampton tunnel were approximately twice those in the Milano tunnel, particularly at the larger apparent wind angles, associated with sailing at a wider angle to the wind, where the lift was lower and the drag due to separation was higher. In retrospect the wake blockage corrections applied to the MEL data are low compared to those applied to the Milano tunnel data. Some wake blockage could also be retrospectively applied to the Volvo tests. Table 1

Dimensions of the tunnel test sections and model scale.

Tunnel Volvo MEL Soton Milano

Width m 6.6 9 4.57 14

Height m 4.1 2.7 3.65 4

Length m 15.8 20 3.7 35

Model scale See below

ACC 20 18 12.5

W60 15 15

Table 2

Summary of sails tested.

Tunnel name Yacht class Main Area (m2 ) Gennaker Code Area (m2₎ Volvo W60 117 G5 195 G-MH-1B 243 MEL IACCv1 197 CC1 423 Soton IACCv2 215 A1 453 Soton W60 117 ASY73B 300 FASY 215 Milano ACCv5 212 A2 531 Table 3

Calculated values for the apparent wind gradient.

Vs/Vtw (ratio)

Vaw/Vtw (ratio)

Baw Twist Vaw/Vaw10 m

10 m Boom Mast Boom Mast

(deg) (deg) (deg) (ratio) (ratio)

0.6 0.57 118.0 4.9 3.1 0.88 1.10 0.7 0.53 108.4 6.5 4.2 0.89 1.09 0.8 0.50 97.5 8.0 5.3 0.91 1.08 0.9 0.50 86.1 8.8 6.1 0.94 1.06 1.0 0.52 75.0 8.9 6.5 0.97 1.04 1.1 0.55 64.9 8.3 6.4 1.00 1.02 1.2 0.60 56.3 7.5 6.0 1.02 1.00

Variation of blockage with apparent wind for tests in various tunnels

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 50 70 90 110 130 150

Apparent wind angle - degrees

Wake blockage correction

ACC Milano IACC Soton

IACC MEL Poly. (IACC Soton)

Linear (ACC Milano)

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10. Measurement methods

The results given in this paper were obtained using test methods that were evolved by the Wolfson Unit MTIA over a prolonged period and numerous projects. They were derived from the methods used by the Yacht Research Group at the University of Southampton in the 1960s, described by Marchaj in his classic book Sailing Theory and Practice, but differ considerably due to improved dynamometry, data acquisition, model sail construction, remote winch operation and test procedures,Campbell, 1998.

Different dynamometers were used in the different tunnels but all were calibrated and corrected for interactions with an overall accuracy and repeatability of the order of71%. The models were isolated from the wind tunnel turntables to avoid problems with tare corrections on roll moments due to wake interactions. The measurements included the forces due to the hull, deck, mast, rigging and sails.

The data acquisition system used for these tests displayed in real time the sail forces, measured in body axes. The sail sheeting and spinnaker pole adjustments were made remotely with the wind on, which enabled the sail settings to be optimised and the maximum forces to be sought. Individual test points were obtained by averaging force measurements over a period of time, of the order of 30 s, and each point represents the result of several minutes of sail adjustments using the real time display.

Procedures for downwind sail testing, where heel angles are small, were developed to obtain the maximum driving force that the rig could produce, since this would cause the yacht to sail at its fastest speed downwind therefore real time VPP techniques are not required during downwind wind tunnel tests. Once the sail coefﬁcients were derived the VPP was used to predict apparent wind angles for different true wind speeds, using the wind triangle shown inFig. 1.

Typical results are shown inFig. 4from measurements made with a number of different sail settings at different apparent wind angles. The force data was plotted at the time of the tests and although tests were made at discrete apparent wind angles the forces were presumed to vary smoothly with apparent wind angle so low values could be identi_{ﬁed and sails readjusted in the search} for the maxima. It can be seen that the driving force coefﬁcients are greatest at apparent wind angles between 901 and 1201. The same force data can be transformed from body to wind axes to

produce the lift and drag coefﬁcients shown inFigs. 8 and 9. In addition the centre of effort height can be obtained from the heeling moment measurements, as shown inFig. 13.

The sails are readjusted at each apparent wind angle and, as can be seen inFig. 5, the use of the spinnaker pole results in similar sail geometry relative to the apparent wind direction with quite different sheeting relative to the yacht.

Although the maximum forces are of primary interest for downwind sailing, other useful information on the rig perfor-mance can be extracted from the lower force measurements by plotting the variation of drag coefﬁcients with the square of lift, as shown inFig. 12. Linear trends in the data can be seen, particularly at the lower wind angles of 50–701 and these are attributable to the variation of induced drag due to lift. The reduced lift

Variation of driving with heeling forces IACC in Southampton tunnel

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 -0.5 0.0 0.5 1.0 1.5 2.0

Heeling force coefficient Cy

Driving force coefficient C

x

A1M3 50 A1M3 70 A1M3 90

A1M3 100 A1M3 120 A1M3 140 IACC fit

Fig. 4. Driving and heeling force coefﬁcients.

Fig. 5. Sails set at two apparent wind angles.

Variation of Cl with apparent wind angle fit from all tunnels

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 50 70 90 110 130 150

Lift coefficient Cl

IACC Soton ACC Milano W60 Volvo W60 Soton

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conditions are achieved mainly by adjustment of the mainsail sheeting angle, with this sail acting like a flap to the highly cambered asymmetric sail and there is a range of settings where thisflap causes relatively small changes to any flow separation. It is therefore inferred that the linear variations in drag with the square of lift are associated with invicidflow rather than varia-tions in the viscous boundary layer. The slope of the induced drag line can be used to derive an effective aspect ratio and height or span for the rig that can provide a useful comparison between the tests.

11. Discussion of results

The curves summarising the maximum lift coefﬁcients from all the tests are shown inFig. 6and the associated drag coef_ﬁcient curves inFig. 7.

Given there were differences between the tunnels, wind, yacht design, models and sails over the 16 year test period, as discussed previously, it is remarkable that the maximum lift coefﬁcient curves are all similar within a 10% band. All the tests showed the maximum lift coefﬁcient to occur at apparent wind angles between 501 and 701 and to be slightly lower at 901.

Maximum lift was sought at 901 since this will have produced maximum driving force so there is probably something associated with the sail geometry and sail interaction that enabled higher lift to be achieved at the closer angles and also for the lift to reduce at wider angles. The side shrouds limit the boom sheeting angle to less than 90_{1 from the yacht’s centreline, which may have} restricted the lift at deeper apparent wind angles.

The drag coefﬁcient curves show greater variation than the lift curves of approximately 20% and with the opposite trend of drag increasing with apparent wind angle. The factors inﬂuencing these differences are considered further.

All of the tests show variations in the results. These variations are considerably greater than measurement uncertainties so they reﬂect the effect of different sail geometries, produced by adjust-ments to the sail sheets and gennaker pole position, on the aerodynamic forces.

Comparison of lift and drag from the two different tests in the Soton tunnel on the W60 and IACC models produced similar maximum lift and drag curves with slightly lower values from the W60. Both these tests included reduced lift settings, although

conducted at slightly different apparent wind angles, and the variation of drag coefﬁcient with the square of lift is shown in Figs. 12 and 20. The effective rig heights from the slope of the induced drag lines were very similar, being 89% of the mast height above the water-line for the IACC rig and 90% for the W60 rig. These are lower than the effective rig heights used for upwind rigs, although these have some form of deck sealing.

The intercept of the induced drag line at zero lift can be considered to be the base drag, including viscous drag, windage from the hull and rigging and any drag due to separation that does not vary due to lift. There was an apparent increase in base drag with increasing apparent wind angles, as can be seen fromFig. 12 by the difference in the parallel lines from the IACC tests at apparent wind angles of 50 and 701. This may be caused by

Variation of Cd with apparent wind angle fits from tunnels

0.0 0.2 0.4 0.6 0.8 1.0 1.2 50 70 90 110 130 150

Drag coefficient Cd

IACC Soton ACC Milano W60 Volvo W60 Soton

Fig. 7. Summary of maximum drag coefﬁcients.

VariationofClwithapparentwindangle IACCinSouthamptontunnels 00 02 04 06 08 10 12 14 16 18 50 70 90 110 130 150 Apparentwindangledegrees Lift coefficient Cl

MEL70 MEL90 MEL110

A1M350 A1M370 A1M390

A1M3100 A1M3120 A1M3140 IACCfit

Fig. 8. Lift coefﬁcients from IACC tests in Soton tunnel.

Variation of Cd with apparent wind angle IACC in Southampton tunnels

0.0 0.2 0.4 0.6 0.8 1.0 1.2 50 70 90 110 130 150

Drag coefficient C

d

MEL 70 MEL 90 MEL 110

A1M3 50 A1M3 70 A1M3 90

A1M3 100 A1M3 120 A1M3 140

IACC windage IACC fit

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increased separatedﬂow off the gennaker at higher apparent wind angles.

The drag due to windage of the hull and rig was measured with the sails removed and is shown inFig. 9and 12 and it can be seen that it is relatively small compared to both the total sail drag and the residual base drag after subtraction of the induced drag.

The W60 fractional gennaker (labelled FASY in theﬁgures) and masthead gennaker (labelled ASY73B) produced similar lift and drag coefﬁcients but it can be seen fromFig. 21that their centre of effort heights were distinctly different. The centre of effort only varied with apparent wind angle by a few per cent but it can be seen by comparing Figs. 13 and 21that the IACC tests produced slightly higher centres of effort.

The IACC tests in the MEL tunnel produced only a few max-imum lift points compared to the complete IACC tests conducted in the Soton tunnel so the results are shown plotted together in

Figs. 8,9,12 and 13. Ltd., Great Britain wind angle of 1101 and the

drag approximately 10% lower. It is possible that the wake blockage was underestimated at the apparent wind angle of 1101, as discussed previously, however whilst increasing the

correction could improve correlation in lift it would reduce the drag. The centre of pressure was higher from the MEL tests, particularly at the problematic apparent wind angle of 1101, and this may be attributed to the boundary layer shown inFig. 2.

Data from the W60 tests in the Soton and Volvo tunnels are shown inFigs. 16–23for ease of comparison and are in addition to data from the IACC tests in the Soton tunnel, shown inFigs. 8

and 9. Lift and drag coefﬁcients were similar at an apparent wind

angle of 901 but were lower from the Volvo tunnel at lower apparent wind angles and higher at higher angles except for a single test point at an angle of 501. This point has both higher lift and drag than the curveﬁt though the data set but it can be seen

from Fig. 22 that the drag is consistent with the increase in

induced drag due to lift. It is therefore possible that the sails were not set in the Volvo tests to produce the maximum lift, except at this single point. It can be seen from Figs. 20 and 22 that the

Variation of Cl with apparent wind angle ACC in Milano tunnel

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 50 70 90 110 130 150

A2 60 A2 75 A2 90

A2 105 A2 120 ACC fit

Fig. 10. Lift coefﬁcients from ACC tests in Milano tunnel.

Variation of Cd with apparent wind angle ACC in Milano tunnel

0.0 0.2 0.4 0.6 0.8 1.0 1.2 50 70 90 110 130 150

d

A2 60 A2 75 A2 90

A2 105 A2 120 ACC fit

Fig. 11. Drag coefﬁcients from ACC tests in Milano tunnel.

Variation of drag with square of lift IACC in Southampton tunnels

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0

lift coefficient squared Cl2

MEL 70 MEL 90 MEL 110

A1M3 50 A1M3 70 A1M3 90

A1M3 100 A1M3 120 A1M3 140

Windage IACC Cdi Cdi

IACC fit

Fig. 12. Lift and drag from IACC tests in Soton tunnel.

Variation of Ceh with apparent wind angle IACC in Southampton tunnels

20 25 30 35 40 45 50 55 60 50 70 90 110 130 150

Centre of effort height above DWL %

MEL 70 MEL 90 MEL 110 A1M3 50 A1M3 70 A1M3 90 A1M3 100 A1M3 120 A1M3 140

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induced drag from the effective rig height obtained from the Soton tests at an apparent wind angle of 60_{1 also matched the Volvo test} results at 40 and 501, albeit with lower base drag. It is possible that the absence of any blockage correction to the Volvo tunnel data inﬂuenced the higher lift and drag data at the apparent wind angle of 901.

Two different sized gennakers were tested in the Volvo tunnel and slightly higher drag coefﬁcients were measured from the smaller G5B. There centre of effort heights were similar, although the G5B was recorded to be a fractional gennaker, but the height tended to decrease with apparent wind angle, not remain constant as from the other tunnel tests. It is possible that there was a roll moment measurement problem.

Data from the IACC tests in the Soton tunnel and the ACC tests in the Milano tunnel are shown in adjacentFigs. 8-11for ease of comparison. The Milano tests were the most recent and used the

Variation of drag with square of lift ACC in Milano tunnel

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Lift coefficient squared Cl2

A2 60 A2 75 A2 90

A2 105 A2 120 ACC fit

Fig. 14. Lift and drag from ACC tests in Milano tunnel.

Variation of Ceh with apparent wind angle ACC in Milano tunnel

20 25 30 35 40 45 50 55 60 50 70 90 110 130 150

Centre of effort above DWL -

%

A2 60 A2 75 A2 90 A2 105 A2 120 Fig. 15. Centre of effort height from ACC tests in Milano tunnel.

Variation of Cl with apparent wind W60 in Southampton tunnel 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 40 60 80 100 120 140

FASY 60 FASY 80 FASY 100

ASY73B 60 ASY73B 85 ASY73B 110 ASY73B 135 Soton W60 fit

Fig. 16. Lift coefﬁcients from W60 tests in Soton tunnel.

Variation of Cd with apparent wind W60 in Southampton tunnel 0.0 0.2 0.4 0.6 0.8 1.0 1.2 40 60 80 100 120 140

d

Fig. 17. Drag coefﬁcients from W60 tests in Soton tunnel.

Variation of Cl with apparent wind W60 in Volvo tunnel 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 40 60 80 100 120 140

G-MH-1B 40 G-MH-1B 50 G-MH-1B 70 G-MH-1B 90 G-MH-1B 110 G5B 40

G5B 50 G5B 60 G5B 70

G5B 80 G5B 90 Volvo fit

(9)

largest model in the biggest tunnel and were undertaken with great care as part of a comprehensive 14 week test programme.

It can be seen that both the lift and drag were lower from the Milano tests and the centre of effort was slightly higher. It is possible that either the wind gradient or twist reduced the maximum lift coefﬁcient from the Milano tunnel with, as dis-cussed previously, an associated reduction in induced drag. Although different apparent wind angles were used in the Soton and Milano tests it can be seen from inspection of lift and drag data inFigs. 12 and 14that the Milano data matched the Soton data at comparable values of lift (Fig. 15).

The Milano tests were focused on achieving the maximum sail force in order to compare different gennaker shapes, so there were not many reduced lift points to use to compare induced drag and effective rig heights with those from the Soton tests. It is, however, notable fromFig. 14the concentration of lift and drag coefﬁcients

from tests over a wide range of apparent wind angles compared to the spread of driving and heeling forces shown inFig. 4. There is a similar concentration of data from the W60 Volvo tests shown in Fig. 22, particularly at reduced values of lift. The effect of the apparent wind angle on the aerodynamic coefﬁcients is secondary to its effect on the transformation of the aerodynamic force vector from wind axes to body axes.

Finally, it is possible that higher lift coefficients were obtained from the Soton tunnel because of thefine scale turbulence induced into theflow by the smoothing screens immediately upstream of the model, which was a unique feature of this tunnel. The onset of flow separation can be delayed or its extent reduced with increasing Reynolds number andfine scale turbulence can cause an effective increase in Reynolds number. It is also possible that full scale maximum lift coefficients could be higher than those measured in any of the wind tunnels, due to Reynolds number effects, but they should not be lower.

Variation of Cd with apparent wind W60 in Volvo tunnel 0.0 0.2 0.4 0.6 0.8 1.0 1.2 40 60 80 100 120 140

G5B 50 G5B 60 G5B 70

G5B 80 G5B 90 Volvo fit

Fig. 19. Drag coefﬁcients from W60 tests in Soton tunnel.

Variation of drag with square of lift W60 in Southampton tunnel 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Square of lift coefficient Cl2

Fig. 20. Lift and drag from W60 tests in Soton tunnel.

Variation of centre of effort with apparent wind, W60 in Southampton tunnel

20 25 30 35 40 45 50 55 60 40 60 80 100 120 140

Ce n tr e o f e ff o r t to DW L %

FASY 60 FASY 80 FASY 100 ASY73B 60 ASY73B 85 ASY73B 110 ASY73B 135

Fig. 21. Centre of effort height from W60 tests in Soton tunnel.

Variation of drag with square of lift W60 in Volvo tunnel 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Square of lift coefficient Cl2

Drag coefficient C d G-MH-1B 40 G-MH-1B 50 G-MH-1B 70 G-MH-1B 90 G-MH-1B 110 G5B 40 G5B 50 G5B 60 G5B 70 G5B 80 G5B 90 Volvo fit

(10)

12. Conclusions

Consistency has been found in the maximum lift coefﬁcient obtained from the different wind tunnel tests on downwind sails within a band of 10% across the range of apparent wind angles associated with downwind sailing.

Induced drag is associated with the lift produced by the downwind sails with an associated effective rig height of approxi-mately 90% of the mast height above the water-line, which is lower than associated with upwind sails. This induced drag accounts for some of the 20% variation in the maximum drag coefﬁcients obtained from the different wind tunnel tests.

There were similar trends in the variation of lift and drag with apparent wind angle from each of the wind tunnels, indicating the validity of these trends. These trends showed a reduction in the maximum lift coefﬁcient with increasing apparent wind angle and an increase in the drag coefﬁcient, with part of this increase associated with the base drag.

There were variations in the centre of effort height that could be attributed to the different wind gradients in the tunnels.

Lower maximum lift coefﬁcients were obtained from the Milano tunnel, which may be attributed to the wind gradient and twist simulated in this tunnel or it is possible thatﬁne scale turbulence in the Soton tunnel allowed higher maximum lift to be achieved.

The applied wake blockage corrections appear to have aided the correlation of sail coef_{ﬁcients obtained from different wind} tunnels.

The effects of apparent wind angle on aerodynamic coefficients, defined in the wind axes, are smaller than those in the driving and heeling force coefficients, defined on the body axes.

The general similarity in the sail coefﬁcients obtained from the different tests in different wind tunnels helps validate the techni-que of wind tunnel testing of sailing yacht rigs.

13. Wind tunnel results

The following figures contain results from each of the five different tests of lift and drag coef_{ficients and centre of effort} height.

Acknowledgements

It has only been possible to publish the previously conﬁdential results due to the kind permission of Sir Michael Fay, Mr. Bruce Farr, Mr. Laurie Smith, Dr. Peter Van Oossanen and Sig Patrizio Bertelli. The work was originally performed for the organisations they represented and were instrumental in creating, all with the common aim of winning prestigious yacht races.

The original tests were conducted with the assistance from colleagues at the Wolfson Unit MTIA and the University of South-ampton together with that of the staff from the organisations operating the different wind tunnels.

Thanks are also extended to the sailmakers associated with each project for designing and manufacturing the model sails. References

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Tahara, T., Masuyama, Y., Fukasawa, Katori, M., 2012. CFD calculation of downwind sail performance using ﬂying shape measured by wind tunnel test. In: Proceedings of HPYD4 Conference, Auckland.

Teeters, J., Ranzenbach, R., Prince, M., 2003. Changes to sail aerodynamics in the IMS rule. In: Proceedings of the 16th Chesapeake Sailing Yacht Symposium.

Viola, I.M., Flay, R.G.J., 2011. Sail pressures from full-scale, wind-tunnel and numerical investigations. Ocean Eng. 38, 1733–1743.

Wright, S., Claughton, A., Paton, J., Lewis, R., 2010, Off-wind sail performance prediction and optimisation. In: Proceedings of the 2nd International Con-ference on Innovation in High Performance Sailing Yachts (INNOVSAIL), Lorient, France.

Zasso, A., Fossati, F., Viola, I.M., 2005. Twistedﬂow wind tunnel design for testing yacht sails. In: Proceedings of the 4th European and African Conference on Wind Engineering (EACWE4), Prague, Czech Republic.

Variation of Ceh with apparent wind W60 in Volvo tunnel 20 25 30 35 40 45 50 55 60 40 60 80 100 120 140

Centre of effort to DWL - %

G5B 50 G5B 60 G5B 70

G5B 80 G5B 90